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Euclidean Distance Location-Allocation Problems with Uniform Demands over Convex Polygons

Author

Listed:
  • Tom M. Cavalier

    (The Pennsylvania State University, University Park, Pennsylvania)

  • Hanif D. Sherali

    (Virginia Polytechnic Institute and State University, Blacksburg, Virginia)

Abstract

In this paper we consider location-allocation problems in which the region to be served is a convex polygon having a uniform demand distribution. Both single and multifacility formulations are considered. For the single facility problem, an algorithm which uses an efficient implementation of the Weiszfeld technique is developed and is shown to converge to a global optimal solution. This analysis is extended to the nonconvex multifacility case. However, although global optimality of the fixed point that the algorithm converges to is not guaranteed, a method suggested for finding a good starting solution increases the likelihood of finding an optimal solution. Extensions of the above problems to include discrete demand points and computational experience are also provided.

Suggested Citation

  • Tom M. Cavalier & Hanif D. Sherali, 1986. "Euclidean Distance Location-Allocation Problems with Uniform Demands over Convex Polygons," Transportation Science, INFORMS, vol. 20(2), pages 107-116, May.
    • Handle: RePEc:inm:ortrsc:v:20:y:1986:i:2:p:107-116
    DOI: 10.1287/trsc.20.2.107
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    Cited by:

    1. Byrne, Thomas & Kalcsics, Jörg, 2022. "Conditional facility location problems with continuous demand and a polygonal barrier," European Journal of Operational Research, Elsevier, vol. 296(1), pages 22-43.
    2. James F. Campbell, 1992. "Location‐allocation for distribution to a uniform demand with transshipments," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(5), pages 635-649, August.
    3. Hanif D. Sherali & Intesar Al-Loughani & Shivaram Subramanian, 2002. "Global Optimization Procedures for the Capacitated Euclidean and l p Distance Multifacility Location-Allocation Problems," Operations Research, INFORMS, vol. 50(3), pages 433-448, June.
    4. Tsao, Yu-Chung & Mangotra, Divya & Lu, Jye-Chyi & Dong, Ming, 2012. "A continuous approximation approach for the integrated facility-inventory allocation problem," European Journal of Operational Research, Elsevier, vol. 222(2), pages 216-228.
    5. Igor Averbakh & Oded Berman & Jörg Kalcsics & Dmitry Krass, 2015. "Structural Properties of Voronoi Diagrams in Facility Location Problems with Continuous Demand," Operations Research, INFORMS, vol. 63(2), pages 394-411, April.
    6. Lozano, S. & Guerrero, F. & Onieva, L. & Larraneta, J., 1998. "Kohonen maps for solving a class of location-allocation problems," European Journal of Operational Research, Elsevier, vol. 108(1), pages 106-117, July.

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